where \(r_i\)  is the real-space position vector of site \(i\) , \(S_j^z\)  is the localized spin operator (\(z\)  component), and \(N\)  is the total number of sites. The transient QFI \(f_\mathrm {Q}(q, t)\)  is completely determined by the instantaneous wavefunction \(|\psi (t)\rangle \) . However, different from the integral relation for equilibrium states [1]}, one cannot obtain the \(f_\mathrm {Q}(q, t)\)  by directly integrating an instantaneous pump-probe spectrum at time \(t\) . We describe here a strategy to extract the time-dependent QFI from a sequence of nonequilibrium spectra.
